Mathematics, Ideas and the Physical Real

Author: Albert Lautman

Publisher: A&C Black

ISBN: 1441144331

Category: Philosophy

Page: 352

View: 4157

Albert Lautman (1908-1944) was a French philosopher of mathematics whose work played a crucial role in the history of contemporary French philosophy. His ideas have had an enormous influence on key contemporary thinkers including Gilles Deleuze and Alain Badiou, for whom he is a major touchstone in the development of their own engagements with mathematics. Mathematics, Ideas and the Physical Real presents the first English translation of Lautman's published works between 1933 and his death in 1944. Rather than being preoccupied with the relation of mathematics to logic or with the problems of foundation, which have dominated philosophical reflection on mathematics, Lautman undertakes to develop an understanding of the broader structure of mathematics and its evolution. The two powerful ideas that are constants throughout his work, and which have dominated subsequent developments in mathematics, are the concept of mathematical structure and the idea of the essential unity underlying the apparent multiplicity of mathematical disciplines. This collection of his major writings offers readers a much-needed insight into his influence on the development of mathematics and philosophy.

Essays on Deleuze

Author: Daniel W Smith

Publisher: Edinburgh University Press

ISBN: 0748655379

Category: Philosophy

Page: 480

View: 8725

Brings together 18 key essays, plus two completely new essays, by one of the world's leading commentators on the work of the French philosopher Gilles Deleuze.

Badiou and Philosophy

Author: Sean Bowden

Publisher: Edinburgh University Press

ISBN: 0748668330

Category: Philosophy

Page: 288

View: 7451

This collection of thirteen essays engages directly with the work of Alain Badiou, focusing specifically on the philosophical content of his work and the various connections he established with both his contemporaries and his philosophical heritage.

Philosophy of Mathematics

Author: N.A

Publisher: Elsevier

ISBN: 9780080930589

Category: Philosophy

Page: 733

View: 4543

One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics. -Comprehensive coverage of all main theories in the philosophy of mathematics -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included

Empiricism, Logic and Mathematics

Philosophical Papers

Author: Hans Hahn

Publisher: Springer Science & Business Media

ISBN: 9400989822

Category: Science

Page: 142

View: 6591

The role Hans Hahn played in the Vienna Circle has not always been sufficiently appreciated. It was important in several ways. In the ftrst place, Hahn belonged to the trio of the original planners of the Circle. As students at the University of Vienna and throughout the fIrst decade of this century, he and his friends, Philipp Frank and Otto Neurath, met more or less regularly to discuss philosophical questions. When Hahn accepted his fIrSt professorial position, at the University of Czernowitz in the north east of the Austrian empire, and the paths of the three friends parted, they decided to continue such informal discussions at some future time - perhaps in a somewhat larger group and with the cooperation of a philosopher from the university. Various events delayed the execution of the project. Drafted into the Austrian army during the first world war" Hahn was wounded on the Italian front. Toward the end of the war he accepted an offer from the University of Bonn extended in recognition of his remarkable 1 mathematical achievements. He remained in Bonn until the spring of 1921 when he returm:d to Vienna and a chair of mathe matics at his alma mater. There, in 1922, the Mach-Boltzmann professorship for the philosophy of the inductive sciences became vacant by the death of Adolf Stohr; and Hahn saw a chance to realize his and his friends' old plan.

Teaching Mathematics in the Block

Author: Susan Nicodemus Gilkey,Carla Herndon Hunt

Publisher: Eye On Education

ISBN: 9781883001513

Category: Education

Page: 186

View: 8718

Provides detailed instructional strategies, sample lesson plans, and sample assessments so that mathematics teachers can make the best use of the additional time.

The Ideal and the Real

An Outline of Kant’s Theory of Space, Time and Mathematical Construction

Author: A. Winterbourne

Publisher: Springer Science & Business Media

ISBN: 9400914156

Category: Philosophy

Page: 139

View: 8529

Many students coming to grips with Kant's philosophy are understandably daunted not only by the complexity and sheer difficulty of the man's writings, but almost equally by the amount of secondary literature available. A great deal of this seems to be - and not only on first reading - just about as difficult as the work it is meant to make more accessible. Any writer deliberately setting out to provide an authentically introductory text thus faces a double problem: how to provide an exegesis which would capture some of the spirit of the original, without gross and misleading over-simplification; and secondly, how to anchor the argument in the best and most imaginative secondary literature, yet avoid the whole project appearing so fragmented as to make the average book of chess openings seem positively austere. Until fairly recently, matters were made even more difficul t, in that commentaries on Kant were very often of a whole work, say, The Critique of Pure Reason, with the result that students would have to struggle through a very great deal of material indeed in order to feel any confidence at all that they had begun to understand the original writings. Recently, things have changed somewhat. There are now excellent commentaries on "Kant's Analytic", "Kant's Analogies" etc. . We have also seen, (at least as reflected in book titles), a resurgence of interest in what is perhaps the most controversial and far-reaching Kantian claim, viz.

Mathematics and the Physical World

Author: Morris Kline

Publisher: Courier Corporation

ISBN: 0486136310

Category: Mathematics

Page: 512

View: 5304

Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.

The Oxford Book of Children's Verse in America

Author: Donald Hall

Publisher: Oxford Books of Verse

ISBN: 0195067614

Category: Juvenile Nonfiction

Page: 319

View: 7976

A collection of American poems written for children or traditionally enjoyed by children, by such authors as Longfellow, Poe, Eugene Field, Langston Hughes, Dr. Seuss, and Jack Prelutsky.

On True and False Ideas

Author: Antoine Arnauld,Stephen Gaukroger

Publisher: Manchester University Press

ISBN: 9780719032035

Category: Cognition

Page: 239

View: 7835

This is an English translation of Arnauld's philosophical reply to Malebranche's Search After Truth. It forms the core of one of the most important philosophical controversies of the 17th century, and one which was to have an impact on 18th-century philosophy, especially in Britain. The translation is accompanied by an introductory essay which looks at the history of the problem of perceptual cognition up until the dispute between Arnauld and Malebranche. The subsequent exchanges between the two are discussed in an appendix.

David Hilbert and the Axiomatization of Physics (1898–1918)

From Grundlagen der Geometrie to Grundlagen der Physik

Author: L. Corry

Publisher: Springer Science & Business Media

ISBN: 1402027788

Category: Science

Page: 513

View: 5128

David Hilbert (1862-1943) was the most influential mathematician of the early twentieth century and, together with Henri Poincaré, the last mathematical universalist. His main known areas of research and influence were in pure mathematics (algebra, number theory, geometry, integral equations and analysis, logic and foundations), but he was also known to have some interest in physical topics. The latter, however, was traditionally conceived as comprising only sporadic incursions into a scientific domain which was essentially foreign to his mainstream of activity and in which he only made scattered, if important, contributions. Based on an extensive use of mainly unpublished archival sources, the present book presents a totally fresh and comprehensive picture of Hilbert’s intense, original, well-informed, and highly influential involvement with physics, that spanned his entire career and that constituted a truly main focus of interest in his scientific horizon. His program for axiomatizing physical theories provides the connecting link with his research in more purely mathematical fields, especially geometry, and a unifying point of view from which to understand his physical activities in general. In particular, the now famous dialogue and interaction between Hilbert and Einstein, leading to the formulation in 1915 of the generally covariant field-equations of gravitation, is adequately explored here within the natural context of Hilbert’s overall scientific world-view. This book will be of interest to historians of physics and of mathematics, to historically-minded physicists and mathematicians, and to philosophers of science.

What is Mathematics?

An Elementary Approach to Ideas and Methods

Author: Richard Courant,Herbert Robbins,Ian Stewart

Publisher: Oxford University Press, USA

ISBN: 9780195105193

Category: Mathematics

Page: 566

View: 5476

A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning.

Scenes from the History of Real Functions

Author: F.A. Medvedev

Publisher: Birkhäuser

ISBN: 3034886608

Category: Mathematics

Page: 265

View: 9797

To attempt to compile a relatively complete bibliography of the theory of functions of a real variable with the requisite bibliographical data, to enumer ate the names of the mathematicians who have studied this subject, exhibit their fundamental results, and also include the most essential biographical data about them, to conduct an inventory of the concepts and methods that have been and continue to be applied in the theory of functions of a real variable ... in short, to carry out anyone of these projects with appropriate completeness would require a separate book involving a corresponding amount of work. For that reason the word essays occurs in the title of the present work, allowing some freedom in the selection of material. In justification of this selection, it is reasonable to try to characterize to some degree the subject to whose history these essays are devoted. The truth of the matter is that this is a hopeless enterprise if one requires such a characterization to be exhaustively complete and concise. No living subject can be given a final definition without provoking some objections, usually serious ones. But if we make no such claims, a characterization is possible; and if the first essay of the present book appears unconvincing to anyone, the reason is the personal fault of the author, and not the objective necessity of the attempt.

Vertex Operator Algebras in Mathematics and Physics

Author: Stephen Berman

Publisher: American Mathematical Soc.

ISBN: 9780821871447

Category: Mathematics

Page: 249

View: 4188

Vertex operator algebras are a class of algebras underlying a number of recent constructions, results, and themes in mathematics. These algebras can be understood as ''string-theoretic analogues'' of Lie algebras and of commutative associative algebras. They play fundamental roles in some of the most active research areas in mathematics and physics. Much recent progress in both physics and mathematics has benefited from cross-pollination between the physical and mathematical points of view. This book presents the proceedings from the workshop, ''Vertex Operator Algebras in Mathematics and Physics'', held at The Fields Institute. It consists of papers based on many of the talks given at the conference by leading experts in the algebraic, geometric, and physical aspects of vertex operator algebra theory. The book is suitable for graduate students and research mathematicians interested in the major themes and important developments on the frontier of research in vertex operator algebra theory and its applications in mathematics and physics.

Where Mathematics Comes from

How the Embodied Mind Brings Mathematics Into Being

Author: George Lakoff,Rafael E. Núñez

Publisher: Basic Books (AZ)


Category: Mathematics

Page: 493

View: 5829

Provides an in-depth analysis of the cognitive science of mathematical ideas that argues that conceptual metaphor plays a definitive role in mathematical ideas, exploring such concepts as arithmetic, algebra, sets, logic, and infinity. 20,000 first printing.

A History of Ancient Philosophy II

Plato and Aristotle

Author: Giovanni Reale

Publisher: SUNY Press

ISBN: 9780791405178

Category: Philosophy

Page: 437

View: 5630

In this book Reale presents Plato and Aristotle. At the center of Reale’s interpretation of Plato is the fulcrum of the supersensible, the metaphysical discovery that Plato presented as a result of the Second Voyage. This discovery of the supersensible is, in Reale’s view, not only the fundamental phase of ancient thought, but it also constitutes a milestone on the path of western philosophy. Reale presents Plato in three different dimensions: the theoretic, the mystical-religious, and the political. Each of these components takes on meaning from the Second Voyage. In addition, Reale has shown that only in the light of the Unwritten Doctrines handed down through the indirect tradition, do these three components, and the Second Voyage itself, acquire their full meaning, and only in this way is a unitary conception of Plato’s thought achieved. The interpretation of Aristotle that Reale proposes depends on his interpretation of Plato. Aristotle read without preconceptions is not the antithesis of Plato. Reale points out that Aristotle was unique among thinkers close to Plato, in being the one who developed, at least in part, his Second Voyage. The systematic-unitary interpretation of Aristotle which Reale has previously supported converges with the new systematic-unitary interpretation of Plato. Certain doctrinal positions which are usually reserved to treatments in monographs will be explored, because only in this way can the two distinctive traits of Aristotle’s thought emerge: the way in which he tries to overcome and confirm the Socratic-Platonic positions, and the way in which he formally creates the system of philosophical knowledge.

A Transition to Advanced Mathematics

A Survey Course

Author: William Johnston,Alex McAllister

Publisher: Oxford University Press

ISBN: 9780199718665

Category: Mathematics

Page: 768

View: 9007

A Transition to Advanced Mathematics: A Survey Course promotes the goals of a "bridge'' course in mathematics, helping to lead students from courses in the calculus sequence (and other courses where they solve problems that involve mathematical calculations) to theoretical upper-level mathematics courses (where they will have to prove theorems and grapple with mathematical abstractions). The text simultaneously promotes the goals of a ``survey'' course, describing the intriguing questions and insights fundamental to many diverse areas of mathematics, including Logic, Abstract Algebra, Number Theory, Real Analysis, Statistics, Graph Theory, and Complex Analysis. The main objective is "to bring about a deep change in the mathematical character of students -- how they think and their fundamental perspectives on the world of mathematics." This text promotes three major mathematical traits in a meaningful, transformative way: to develop an ability to communicate with precise language, to use mathematically sound reasoning, and to ask probing questions about mathematics. In short, we hope that working through A Transition to Advanced Mathematics encourages students to become mathematicians in the fullest sense of the word. A Transition to Advanced Mathematics has a number of distinctive features that enable this transformational experience. Embedded Questions and Reading Questions illustrate and explain fundamental concepts, allowing students to test their understanding of ideas independent of the exercise sets. The text has extensive, diverse Exercises Sets; with an average of 70 exercises at the end of section, as well as almost 3,000 distinct exercises. In addition, every chapter includes a section that explores an application of the theoretical ideas being studied. We have also interwoven embedded reflections on the history, culture, and philosophy of mathematics throughout the text.